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Numerical Investigation of the Effect of a Magnetic Field on the Transport of Oxygen in Air

The effects of magnetisation forces in a binary mixture of gases characterised by large differences in magnetic susceptibility are studied using numerical simulations, with a focus on the differential diffusion of the species and the role of the gradient of mixture composition on the flow field resulting from magnetically-induced forces. A quiescent binary mixture of nitrogen and oxygen, representative of air, confined between two parallel plates is considered. In all simulations, a gradient of $\mathbf{B}^2$, the square of the magnetic flux density magnitude, uniform and directed normal to the walls is imposed. Cases characterised by different pressures, different strengths of $\nabla(\mathbf{B}^2)$, and different initial gradients of species composition are investigated, while the same initial temperature is used in all cases. Non-dimensional groups related to the examined configuration are proposed. In cases characterised by an initially uniform mixture composition, species tend to separate and accumulate at opposite walls, due to differential magnetic forces arising from the differences in magnetic susceptibility. For a given strength of $\nabla(\mathbf{B}^2)$, the effect of the magnetic field on the separation of species increases with decreasing pressure.In addition to species separation, it is shown that an initial gradient in the mixture composition perpendicular to $\nabla(\mathbf{B}^2)$ induces a significant change in the velocity field, which enhances the transport of species. This effect is due to a lack of alignment between the gradient of averaged magnetic susceptibility and $\nabla(\mathbf{B}^2)$ and could be exploited to achieve targeted mixing using engineered magnetic fields.